Abstract:
Using the theory of commutative Banach algebras, we find
an estimate of the solution of a higher-order linear differential equation; from this estimate, we derive
a Lyapunov asymptotic stability test for this equation.
Here the results by Faedo and Kharitonov on the Hurwitz conditions
for families of polynomials find a natural application.
Similar statements are obtained
for a system of linear differential equations.
Keywords:commutative Banach algebras, differential equations
in Banach algebras, Lyapunov stability.
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